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On Some Twisted Chevalley Groups Over Laurent Polynomial Rings

Published online by Cambridge University Press:  20 November 2018

Jun Morita
Jun Morita*
Affiliation:
University of Tsukuba, Ibaraki, Japan
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We let Z denote the ring of rational integers, Q the field of rational numbers, R the field of real numbers, and C the field of complex numbers.

For elements e and f of a Lie algebra, [e,f] denotes the bracket of e and f. A generalized Cartan matrix C = (cij) is a square matrix of integers satisfying cii = 2, cij ≦ 0 if i ≠ j, cij = 0 if and only if cji = 0. For any generalized Cartan matrix C = (cij) of size l × l and for any field F of characteristic zero, denotes the Lie algebra over F generated by 3l generators e1, …, el, h1, …, hl, f1, …, fl with the defining relations

for all i, j,

for distinct i, j.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 5 , 01 October 1981 , pp. 1182 - 1201
Copyright
Copyright © Canadian Mathematical Society 1981

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